In order to tame an animal you have to :

- make some food available to it (for boars, drop some shrooms / berries around like Zen explained)
- have it rest in a calm state (no ! on top of it, "no alarms and no surprises").

It usually takes : building a fence, luring it in, going away so it settles down, then approach stealthily, let it eat, hang around ; it should then have some heart <3 popping above it. The heart means the taming process has started. It takes something around 30-45 minutes irl to complete.